A Re-solving Heuristic with Uniformly Bounded Loss for Network Revenue Management

TL;DR

This paper introduces a new re-solving heuristic for network revenue management that maintains a uniformly bounded revenue loss, regardless of the problem size, by strategically re-optimizing the deterministic linear program at selected times.

Contribution

The paper proposes a novel re-solving heuristic with bounded loss, improving upon existing methods that have loss scaling with problem size.

Findings

Frequent re-solving yields similar revenue loss as no re-solving, scaling with the square root of horizon and resources.

Strategic re-solving at selected times with thresholds achieves a constant bound on revenue loss.

The heuristic's performance is robust regardless of problem scale.

Abstract

We consider the canonical (quantity-based) network revenue management problem, where a firm accepts or rejects incoming customer requests irrevocably in order to maximize expected revenue given limited resources. Due to the curse of dimensionality, the exact solution to this problem by dynamic programming is intractable when the number of resources is large. We study a family of re-solving heuristics that periodically re-optimize an approximation to the original problem known as the deterministic linear program (DLP), where random customer arrivals are replaced by their expectations. We find that, in general, frequently re-solving the DLP produces the same order of revenue loss as one would get without re-solving, which scales as the square root of the time horizon length and resource capacities. By re-solving the DLP at a few selected points in time and applying thresholds to the customer acceptance probabilities, we design a new re-solving heuristic whose revenue loss is uniformly bounded by a constant that is independent of the time horizon and resource capacities.